The purpose of the proposed research is to further the development of the mathematical theory for the transport of chemotactic bacteria. Solutions to the initial-value problems associated with the recent experiments of Dahlquist, Lovely and Koshland will be obtained in the proposed research. The boundary-initial value problems for the development of a steadily propagating band of chemotactic bacteria in a capillary tube and a ring in an agar plate, as observed in the experiments by Adler, will also be given detailed and comprehensive treatment. From the latter analyses will emerge theoretical formulas for the band and ring propagation parameters (i.e., velocity, total bacteria number, etc.), which are to be checked with the experimental values. The stability problem for a steadily propagating band in a capillary tube will also be studied in the proposed theoretical investigation. Finally, consideration will be given to the possibility of new chemotactic bacterial transport phenomena predicted by the theory and accessible to observation in future experiments. Of manifest importance to a fundamental understanding of the bacteria themselves, the proposed development of a quantitative theory for bacterial chemotaxis may also serve to aid our understanding of neurobiology and psychology, if it is indeed true that all living organisms are endowed with similar mechanisms for responding to stimuli by movement. Moreover, many species of pathogenic bacteria can be expected to undergo chemotactic migration when subjected to appropriate conditions in vivo, and hence a quantitative theory for bacterial chemotaxis may eventually engender novel clinical methods for treating local bacterial infection in humans by a chemotherapy that involves the chemotactic motion of the pathogenic bacteria.